Double layers form along auroral field lines in the Earth's magnetosphere. They form in order to maintain current continuity in the ionosphere in the presence of a magnetospheric electric field E with nabla x E is not equal to 0. Features which govern the formation of the double layers are: (1) the divergence of E, (2) the conductivity of the ionosphere, and (3) the current-voltage characteristics of auroral magnetic field lines. Astrophysical situations where nabla x E is not equal to 0 is applied to a conducting plasma similar to the Earth's ionosphere are potential candidates for the formation of double layers. The region with nabla x E is not equal to 0 can be generated within, or along field lines connected to, the conducting plasma. In addition to nabla x E, shear neutral flow in the conducting plasma can also form double layers.